Generalized CMB initial conditions with pre-equality magnetic fields

The most general initial conditions of CMB anisotropies, compatible with the presence of pre-equality magnetic fields, are derived. When the plasma is composed by photons, baryons, electrons, CDM particles and neutrinos, the initial data of the truncated Einstein-Boltzmann hierarchy contemplate one magnetized adiabatic mode and four (magnetized) non-adiabatic modes. After obtaining the analytical form of the various solutions, the Einstein-Boltzmann hierarchy is numerically integrated for the corresponding sets of initial data. The TT, TE and EE angular power spectra are illustrated and discussed for the magnetized generalization of the CDM-radiation mode, of the baryon-radiation mode and of the non-adiabatic mode of the neutrino sector. Mixtures of initial conditions are examined by requiring that the magnetized adiabatic mode dominates over the remaining non-adiabatic contributions. In the latter case, possible degeneracies between complementary sets of initial data might be avoided through the combined analysis of the TT, TE and EE angular power spectra at high multipoles (i.e. $\ell >1000$).